Resonance scattering in a waveguide with identical thick barriers

Abstract

We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are almost fully reflected. However, we show the existence of a resonance frequency at which the wave is almost fully transmitted, even for very small holes. This resonance scattering, which is known as tunneling effect in quantum mechanics, is demonstrated in a constructive way by rather elementary tools, in contrast to commonly used abstract methods such as searching for complex-valued poles of the scattering matrix or non-stationary scattering theory. In particular, we derived an explicit equation that determines the resonance frequency. The employed elementary tools make the paper accessible to non-experts and educationally appealing.

Design of a mode converter using thin resonant ligaments

“…The decomposition with the Neumann and Dirichlet problems would be the same and the asymptotic procedure would be very similar. This is an interest of the method proposed here compared for example to the technique of [9,10] based on decomposition in Fourier series or the one of [28,26] relying on integral equations with an explicit kernel, we do not need separation of variables in Π ± . But as already announced in Remarks 6.1, 6.2, for a generic domain, we can not position the ligaments to get (17).…”

“…On the other hand, taking the limit ε → 0 + in the equation (10) restricted to L ε ± , we obtain the problem with Dirichlet BC…”

“…First, we emphasize that the influence of the non resonant ligament L ε + appears only at the next order in ε. This is an important point which allows us to decouple the two problems ( 9) and (10) (at least at first order in ε). Second, we observe that the first terms r N 0 11 , r N 0 12 in the asymptotic of…”